Rigorizing the use of the coefficient of variation to diagnose fracture periodicity and clustering

Abstract

The coefficient of variation (CV), or ratio of a population standard deviation to mean, can distinguish regular spacing (CV < 1) or clustering (CV > 1) from random sequences (CV = 1) in 1D spatial or time-series data. This technique is commonly applied to fracture spacing, with qualitative interpretations of the significance of the regularity or clusteredness. Here we use Monte Carlo simulations to derive robust confidence intervals for distinguishing 1D patterns from random signals using CV. Our simulations show that CV is negatively skewed for small fracture populations. We also present a new alternative statistic, CV’, which is unbiased and retains the capability of CV to distinguish nonrandomness in 1D sequences.